Typical HR HD simulations focus on the group core, where the central galaxy contributes to a substantial amount of metals later dispersed in the diffuse IGrM, which are mainly produced via supernovae (SN) explosions and winds from red giant stars (SWs). An exemplary and well modeled system is the nearby galaxy group NGC 5044, with the homonymous central galaxy dominating over the many smaller satellites.
In several ETGs/BGGs analytic studies and non-cosmological HD simulations [e.g. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}], a common implementation of Eq. REF  is to recast it in terms of the astrophysical IGrM abundance of the \(i\) th-element (by mass in Solar unit):
\( \frac{Z_i}{t} = (\underbrace{N_\ast \,\alpha _\ast }_{\rm stellar\ winds} + \underbrace{N_{\rm SN}\,\alpha _{\rm SN}}_{\rm supernovae})\,\frac{\rho _\ast }{\rho },\) 
